7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Find the slope of the line through each pair of points. Warm Up Find the slope of the line through each pair of points. 1. (1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation. 3. 4x + 5x + 6x = 45 4. (x – 5)2 = 81 5. Write in simplest form. 2 x = 3 x = 14 or x = –4

In a ratio, the denominator of the fraction cannot be zero because division by zero is undefined. Remember!

A ratio can involve more than two numbers A ratio can involve more than two numbers. For the rectangle, the ratio of the side lengths may be written as 3:7:3:7.

A proportion is an equation stating that two ratios are equal.

In the proportion , the values a and d are the extremes. When the proportion is written as a:b = c:d, the extremes are in the first and last positions.

In the proportion , the values b and c are the means. When the proportion is written as a:b = c:d, the means are in the two middle positions.

In Algebra 1 you learned the Cross Products Property In Algebra 1 you learned the Cross Products Property. The product of the extremes ad and the product of the means bc are called the cross products. The Cross Products Property can also be stated as, “In a proportion, the product of the extremes is equal to the product of the means.” Reading Math

Example 1: Writing Ratios Write a ratio expressing the slope of l. Substitute the given values. Simplify.

Example 2: Using Ratios The ratio of the side lengths of a triangle is 4:7:5, and its perimeter is 96 cm. What is the length of the shortest side? Side lengths 4x,7x, 5x Combine like terms 4x + 7x + 5x = 96 Simplify 16x = 96 Divide both sides by 16. x = 6 Substitute (6) for x 4x = 4(6) = 24 cm The length of the shortest side is 4x = 4(6) = 24 cm.

Example 3: Solving Proportions Solve the proportion. 7(72) = x(56) Cross Products Property 504 = 56x Simplify. x = 9 Divide both sides by 56.

Example 4: Solving Proportions Solve the proportion. (z – 4)2 = 5(20) Cross Products Property (z – 4)2 = 100 Simplify. (z – 4) = 10 Find the square root of both sides. Rewrite as two eqns. (z – 4) = 10 or (z – 4) = –10 z = 14 or z = –6 Add 4 to both sides.

Example 5: Using Properties of Proportions Given that 18c = 24d, find the ratio of d to c in simplest form. 18c = 24d Divide both sides by 24c. Simplify.

Example 6: Problem-Solving Application Marta is making a scale drawing of her bedroom. Her rectangular room is 12 feet wide and 15 feet long. On the scale drawing, the width of her room is 5 inches. What is the length? The answer will be the length of the room on the scale drawing.

Example 6 Continued or 5(15) = x(12.5) Cross Products Property 75 = 12.5x Simplify. x = 6 Divide both sides by 12.5. The length of the room on the scale drawing is 6 inches.

Lesson Quiz 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2. 3. 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building? 15°, 75°, 90° 3 7 or –7 18 in.